#Mark the correct alternative in each of the following
Let f(x) = x3 + 3x2 – 9x + 2. Then f(x) has
f(x)=x3+3x2-9x+2
f’(x)=3x2+6x-9
f’(x)=0
3x2+6x-9=0
by solving the quadratic we get roots as follows
x=-3 and x=1
Hence by second derivative test
f’’(x)>0 or f”(x)<0 so it’s a point of minimum or maximum respecctively.
f”(x)=6x+6
f”(-3)=6(-3)+6
=-12<0
so At x=-3 maximum value.
f”(1)=6+6
=12>0
so At x=1 minimum value.
Option=(B)